Calculations of a Magnetic Gear by the Method of Separation of the Fourier Variables

Abstract

Magnetic gears can be divided into two groups: uncontrollable reducers constructed on permanent magnets and controlled ones that contain, in addition to magnets, the stator winding with a frequency converter. The first group has a fixed coefficient of magnetic reduction, while, for the second group, it can be changed by means of a frequency converter. The suggested field analytical calculation method can be used to determine the functional properties of both types of these devices with a use of two Cartesian coordinates x and y. In each active region of the magnetic gear (air gaps, magnets, stator and rotor yokes, a rotor with through teeth and grooves (modulator)), the sought variables, i.e., magnetic potentials and magnetic inductions, are represented as a product of two functions, the first of which is affected by coordinate x and the other by coordinate y. These functions are also multiplied by some unknown constants, the values of which taken are from the boundary conditions of the magnetic field on the interface lines of active regions. The magnetic permeability of ferromagnetic regions (yoke, modulator rods) are assumed to be fixed, with their values being adjusted according to the calculations of magnetic circuit of the reducer. This approach makes it possible to implement the principle of superposition of magnetic fields formed by the rotor and stator sources, respectively. In this case, the calculations of the unknown constants are carried out twice for each source, since the latter have fundamentally different numbers of poles and, hence, have a different spectrum of harmonic components of the magnetomotive forces. The proposed method makes it possible to determine the magnetic inductions in working air gaps of the magnetic gear and the electromagnetic moments that act on the rotors and the stator. The results were confirmed by the experimental data. To implement the method, a set of functions available in the Mathcad mathematical program is enough.